How are fractions reduced to their simplest form?


Quick Answer

Reduce fractions to their simplest form by simplifying the fraction in a series of division steps. The other way is to divide the top and bottom numbers by their greatest common factor.

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Full Answer

In the first method, check whether the numerator and denominator of the fraction both end in zero. If so, divide both numbers by 10. Repeat this until one or both numbers no longer end in zero. If one or both numbers end in five, or if one ends in five and the other in zero, divide both numbers by five.

Next, if both numbers are even, divide both by two. To see whether the numerator and denominator are divisible by three, add the digits in each number. If the total is three or a multiple of three, divide both numbers by three. Check to see whether the top and bottom numbers are evenly divisible by seven or 11, and if both are, divide by that number.

To simplify using the greatest common factor, first find all the factors of the numerator. Look for all the prime numbers that multiply together to make the number. The factors of 60 are 2 x 2 x 3 x 5. Do the same thing for the denominator. If the denominator is 150, its prime factors are 2 x 3 x 5 x 5.

Now see which numbers the numerator and denominator have in common. Here, both 60 and 150 have two, three and five in common. Multiplying these together gives 30, which is the greatest common factor.

To simplify the fraction, divide both top and bottom (60/150) by the greatest common factor, 30. For example: 60/30 = 2 and 150/30 = 5. So the simplified fraction is 2/5.

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